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academic year 2009/2010

PROGRAMMING AND COMPUTING LABORATORY
instructor: Stefano Finzi Vita

Degree courses: Mathematics - DM 270/04 (three years)
Mathematics - DM 509/99 (three years)
Tipo di attività formativa: di base
Credits: 9
Scientific sector: MAT/08
Teaching language: italiano
TRADURRE Canale: Dl-Pa
Period: I semester ( sep 28, 2009 - jan 12, 2010)


Aula ed orario di lezione

Tutoring: in LAB1 - LUN ore 11:00-13:00

Presence: highly recommended

Module aims:
The main goal is to introduce the students to a constructive approach to mathematics also by meansof personal computers. In this respect, the course complements other courses of the first year wherethe logic/deductive point of view is more emphasized.A major part of this course will be devoted to problem solving, to the analysis of basic algorithms and to their implementation in C.

Module subject:
The main topics are:
1. Introduction to the C++ language: structure of a C++ program, types of variables, commands of the pre-compiler, arithmetic and logic operators, pointers, mathematical functions. Input/output. Cicles: for, while, do-while, for. Alternatives: if-else. Matrix and vectors in C. Functions. Graphics commands.
2. Number and functions on a computer. Floating point representation, rounding and truncation errors. Logic operations, Bool algebra. Basic operations on sets. Polynomials, Horner’s algorithm. Taylor expansion. Numerical derivatives.
3. Linear maps in the plane. Linear systems. Gauss method, Jacobi method. Algorithms for computing the determinant and the inverse matrix.
4. Sequences and series. Limit approximation, stopping rule and error. Recursive sequences, fixed point theorem.
5. Root finding. Bisection, Newton’s and secant algorithms. Convergence and a priori error estimates. Order of convergence of Newtons’s method.
6. Polynomial interpolation. Error estimates for linear and quadratic interpolation. Composite Lagrange interpolation.
7. Quadrature formulas. Rectangle, trapezoid and Simpson’s rules. Geometric interpretation. Error estimates.

Detailed module subject: Argomenti svolti a lezione (finale)

Office hours: Solo per gli studenti del corso: LUN ore 14.15-15.15, stanza 17 (piano terra)

Suggested readings:

Issues:

Type of course: standard

Exercises:

Assessment method: Prove d'esame

Examination tests:

Examination results:

Notices:

Knowledge and understanding: Successful students will be able to
have a basic knowledge of programming and of the mathematical properties of simple algorithms. They will also achieve some fundamental notions about convergence, order of convergence, errors and complexity for elementary algorithms.

Skills and attributes: Successful students will be able to
write a simple C code for scientific purposes and to manage elementary numerical algorithms to solve problems. They will be able to choose the appropriate algorithm for simple problems like finding the root of an equation, computing an integral or solving a linear system.During the laboratory sessions they will learn how to use PCs, graphics tools and a LAN network.

Personal study: the percentage of personal study required by this course is the 65% of the total.

Examination dates:

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